Theory Of Atmospheric Turbulence Research Articles

Influence of sand and dust turbulent atmosphere on performance of free space quantum communication

Quantum communication is a frontier hotspot of current research, and it has ideal information security. In order to enable quantum systems in arid and desertified areas to work almost under all-weather condition, it is necessary to study the attenuation of free-space quantum signal transmission and the influence of the turbulence atmosphere carrying sand and dust on communication performance. Using Mie scattering theory, multiple scattering simulation method, and atmospheric turbulence theory, the attenuation of optical wave transmission in sand and dust turbulent atmospheric channels with different visibility, and the influence of multiple scattering and turbulence on attenuation are studied. The results show that the effect of multiple scattering increases with the decrease of visibility, the turbulence effect gradually strengthens with the increase of distance. According to the quantum amplitude damped channel model, the effects of multiple scattering and turbulence in the sand and dust turbulent atmosphere with different visibility on the quantum channel capacity, fidelity and bit error rate are analyzed. The results show that as the visibility decreases, the multiple scattering effect increases, resulting in the decrease of attenuation and bit error rate, but an increase in channel capacity, fidelity and the boundaries of security key rate. The existence of turbulence in the dust atmosphere will increase the attenuation and bit error rate, but reduce the channel capacity, fidelity and security key rate. It can be seen that the influence of multiple scattering and turbulence on the communication performance, when the visibility of the sand and dust atmosphere are both low, cannot be ignored. In practical applications, the relevant parameters of quantum communication should be adaptively adjusted according to the visibility and turbulence intensity to improve the probability, efficiency and reliability of quantum communication.

Revisiting the global surface energy budgets with maximum-entropy-production model of surface heat fluxes

The maximum-entropy-production (MEP) model of surface heat fluxes, based on contemporary non-equilibrium thermodynamics, information theory, and atmospheric turbulence theory, is used to re-estimate the global surface heat fluxes. The MEP model predicted surface fluxes automatically balance the surface energy budgets at all time and space scales without the explicit use of near-surface temperature and moisture gradient, wind speed and surface roughness data. The new MEP-based global annual mean fluxes over the land surface, using input data of surface radiation, temperature data from National Aeronautics and Space Administration–Clouds and the Earth’s Radiant Energy System (NASA CERES) supplemented by surface specific humidity data from the Modern-Era Retrospective Analysis for Research and Applications (MERRA), agree closely with previous estimates. The new estimate of ocean evaporation, not using the MERRA reanalysis data as model inputs, is lower than previous estimates, while the new estimate of ocean sensible heat flux is higher than previously reported. The MEP model also produces the first global map of ocean surface heat flux that is not available from existing global reanalysis products.

A simple method for evaluating the wavefront compensation error of diffractive liquid-crystal wavefront correctors

A simple method for evaluating the wavefront compensation error of diffractive liquid-crystal wavefront correctors (DLCWFCs) for atmospheric turbulence correction is reported. A simple formula which describes the relationship between pixel number, DLCWFC aperture, quantization level, and atmospheric coherence length was derived based on the calculated atmospheric turbulence wavefronts using Kolmogorov atmospheric turbulence theory. It was found that the pixel number across the DLCWFC aperture is a linear function of the telescope aperture and the quantization level, and it is an exponential function of the atmosphere coherence length. These results are useful for people using DLCWFCs in atmospheric turbulence correction for large-aperture telescopes.

Atmospheric turbulence theory applied to GPS carrier-phase data

Turbulent irregularities in the lower atmosphere cause physical correlations between Global Positioning System (GPS) carrier-phase measurements. Based on turbulence theory, a variance–covariance model is developed in this paper that reflects these correlations. The main result shows that the obtained fully-populated variance–covariance matrices depend not only on the satellite-station geometry, but also on the prevailing atmospheric conditions, which are parameterised by, e.g., the von Karman spectrum of refractivity fluctuations and the wind velocity vector. It is shown that the amount of the correlation between two GPS carrier-phase observations is inversely related to the separation distance of the corresponding ray paths through the turbulent atmosphere. Furthermore, the wind velocity and direction play a key role in the correlation.

The effects of seeing on Sérsic profiles - II. The Moffat PSF

ABSTRA C T The effects of seeing on Sersic r 1/n profile parameters are extensively studied using a Moffat function. This analytical approximation to the point spread function (PSF) is shown to provide the best fit to the PSF predicted from atmospheric turbulence theory when b , 4:765. The Moffat PSF is additionally shown to contain the Gaussian PSF as a limiting case Ob! 1U. The Moffat function is also shown to be numerically well behaved when modelling narrow PSFs in HST images. Seeing effects are computed for elliptically symmetric surface brightness distributions. The widely used assumption of circular symmetry when studying the effects of seeing on intrinsically elliptical sources is shown to produce significant discrepancies with respect to the true effects of seeing on these sources. A prescription to correct raw (observed) central intensities, effective radii, index n and mean effective surface brightness is given.

Spatial interpolation of the atmospheric water vapor content between sites in a ground‐based GPS Network

We have studied three methods of spatially interpolating GPS‐estimated wet delay time series. Five months of data from three sites in the Swedish continuously operating GPS network were used for interpolation to a fourth site. Different geometries were used, resulting in interpolation distances of 40–120 km. To assess the quality of the interpolations we compared the obtained time series with estimated wet delay from a GPS station and with radiosonde data. A method based on the theory of atmospheric turbulence showed the lowest errors when compared to both the GPS estimates and the radiosonde data. The rms errors using this method are typically 1 cm.

TAKING THE TWINKLE OUT OF THE STARS: AN ADAPTIVE WAVEFRONT TILT CORRECTION SERVO AND PRELIMINARY SEEING STUDY FOR SUSI

ABSTRACT The Sydney University Stellar Interferometer (SUSI) at Narrabri N.S.W., Australia, operates at optical wavelengths and has a maximum baseline of 640m. In order to form fringes with this instrument the distortion introduced into the wavefront by the atmosphere must be minimized. In SUSI this is done by restricting the aperture to r0 or less, thereby sampling a basically flat but tilted wavefront. A pair of tip/tilt servos are then used to adjust for angle of arrival. The thesis contains a review of atmospheric turbulence theory including a new approximation for the temporal power spectra for any Zernike coefficient due to Kolmogorov turbulence. The temporal power spectra is calculated using the Taylor hypothesis of frozen turbulence. Unlike previous work of this kind the analysis is performed in the Fourier domain resulting in a solution that does not require numerical integration. A description of the tip/tilt servo follows along with a review of digital servo theory and an analysis of the servo performance. The final section of the thesis deals with atmospheric turbulence measurements made using the system. The tilt correction servo consists of 'pyramid' quadrant detectors and piezo-electrically controlled tip/tilt mirrors. With a sample frequency of 1000 Hz the system measures image position and re-centers the stellar image. Based on measurements of many stellar objects over several nights the system was found to hold the two beams of the interferometer parallel with a standard deviation of 0.164 ± 0.025 arcseconds. With an aperture size of 0.06 meters this implies less than a 2% loss in the visibility measurements made by SUSI. The system has been used on stars as faint as magnitude 6.5 and is predicted to have a limiting magnitude of 7.5 and possibly as high as 8.5. By logging the mirror positions required to center the image a direct measurement of the wavefront phase gradient is obtained. Using this data it is possible to investigate atmospheric turbulence theory and, in particular, the wavefront tilt temporal power spectra. It is shown that at low frequencies the wavefront tilt power spectrum follows the -2/3 power law predicted by the theoretical analysis. At high frequencies the power law becomes -11/3, while the theory predicts -17/3. Since only a small part of the energy of the spectrum is contained in the high frequency domain this is of little practical importance. The difference is due to the fact that the servo measures average phase gradient which is not identical to the Zernike polynomials representing tilt. The system therefore not only corrects for the tilt introduced by the atmosphere but will supply a good estimate of seeing conditions using the same optical path as that used by the visibility measurement system itself. A preliminary investigation of seeing at the Narrabri site was undertaken, resulting in a median r0 value of 7.1-1.6+2.1 cm at a wavelength of 500nm. Based on these measurements the seeing at the site has been shown to have a median of 1.3 seconds of arc with seeing better than 1.5 seconds of arc 75% of the time. These values are consistent with similar seeing studies at other observatory sites.

Remote sensing of atmospheric turbulence and transverse winds from wave-front slope measurements from crossed optical paths

In the theory of atmospheric turbulence, the strength of the spatial variations of the index of refraction n is proportional to a parameter known as the atmospheric-structure constant. The atmosphericstructure constant is denoted C(2)(n)(z) and is a function of position along the optical path z. The characteristics of the temporal variations of the index of refraction are related to both C(2)(n)(z) and to the transverse wind velocity V(z). Current optical techniques for remotely sensing C(2)(n)(z) and V(z) rely primarily on the spatial or temporal cross-correlation properties of the intensity of the optical field. In the remote-sensing technique proposed here, we exploit the correlation properties of the wave-front slope measured from two point sources to obtain profiles of C(2)(n)(z) and V(z). The two sources are arranged to give crossed optical paths. The geometry of the crossed paths and the characteristics of the wave-front slope sensor determine the achievable resolution. The signal-to-noise ratio calculationsindicate the need for multiple measurements to obtain useful estimates of the desired quantities.

Interferometric Measurements of Atmospheric Seeing

AbstractIn conjunction with the Stellar Interferometer project at Sydney University, a shearing interferometer system has been constructed to measure the atmospheric ‘seeing’ in real time using a portable telescope. The interferometric method allows direct measurement of the parameter ro, which derives from the theory of atmospheric turbulence. This permits reliable comparison with ‘seeing’ determinations by other methods. This paper briefly describes the instrument and presents initial results of the observing program.

Tropical Winds Measured by the Arecibo Radar

Abstract Preliminary measurements of tropospheric and stratospheric parameters using the large 430 MHz radar at Arecibo, Puerto Rico, show excellent agreement between a wind profile deduced from the radar back-scatter and a profile obtained simultaneously from a rawinsonde ascent from San Juan. The measured variations of scattered power with altitude agree quite well with predictions of atmospheric turbulence theory.

A suggested test of a theory of atmospheric turbulence

A suggested test of a theory of atmospheric turbulence

Variance of Radio Frequency Caused by Atmospheric Turbulence in Line-of-Sight Transmissions

The frequency stability of a radio signal propagated over a line-of-sight path is reduced by time variations in phase velocity along the path. This instability caused by the atmosphere will produce errors in frequency measurements made by averaging a standard frequency transmission over a period of time T and also in time interval measurements made by counting the number of cycles of the standard frequency received during a period of time T. Recent measurements of the variations in phase of a received signal at microwave frequencies permit estimation of both types of error as a function of T. These atmosphere-induced errors are compared to the errors inherent in the best currently-available cyrstal oscillators and it appears that the latter source of error is dominant for line-of-sight paths through the atmosphere. The level and slope of the frequency spectra have been observed to vary over wide ranges with time and geographical location. The spectral form W(f)~f <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2/3</sup> expected on the basis of the Obukhov-Kolmogorov theory of atmospheric turbulence has a slope which lies will within the range of observed slopes for the range of fluctuation frequencies from 1 cycle/day to 1 cps.

Atmospheric turbulence

AbstractEvidence which has accumulated shows that the classical theory of atmospheric turbulence which assumes that K the coefficient of eddy diffusion is constant with height is inadequate to explain the observed variations of wind and temperature with height. It was shown however by the present writer, 1946, that if K could be represented by a certain power law of the height above the surface it was possible to account for many of the complicated problems of atmospheric diffusion near the earth's surface. In the present paper it is shown that with this power law representation of K it is possible to give a quantitative treatment of the approach of the surface wind to the geostrophic wind. The angle of veer between the surface wind and the isobars is found to be independent of the roughness of the surface and to be dependent only upon the stability. The diurnal variation of wind speed and direction at various heights is discussed on the basis of the present theory and is shown to be in accordance with observations.

Turbulence and diffusion in the lower atmosphere with particular reference to the lateral effect

It has been established experimentally by Pasquill that the theory of atmospheric turbulence put forward by O. G. Sutton in 1934 leads to satisfactory theoretical rates of evaporation from plane, saturated, liquid surfaces. The theory, however, overestimates the vapour concentration at any point and underestimates the rate of decay of concentration with height above such evaporating surfaces of finite lateral dimensions. In the present paper it is suggested that one of the reasons for this discrepancy lies in the neglect of the lateral component of turbulence. The aim of the present investigation is to estimate quantitatively the effect on the values of the theoretical vapour concentration produced by the introduction of a lateral component of turbulence. It is shown that the theoretical evaporation is not appreciably affected by the modification introduced but that the concentration of vapour, and the rate of decay of concentration with height, are much nearer the experimental values, which, however, are very scanty. The investigation deals with a saturated area of parabolic shape. Extensions of the theory are contemplated.

Turbulence and diffusion in the lower atmosphere

The only existing theory of atmospheric turbulence which is capable of giving a quantitative approach to the complex problems of diffusion in the lower atmosphere is the classical theory in which it is generally assumed that the effect of eddies in the atmosphere is completely analogous to that of molecules in a gas apart from a difference of scale. This assumption, which later evidence has shown to be incorrect, is not essential to the theory, and in the present paper is replaced by the assumption that the mixing length of an eddy increases with both height above and nature of the earth’s surface . With this assumption a self-consistent treatment of diffusion is developed which is able to account quantitatively for such meteorological phenomena as the distribution of water vapour over land and sea (including evaporation from the oceans) and the diffusion of smoke near the ground. The treatment is mainly confined to diffusion in an adiabatic atmosphere.

A note on the constancy of horizontal turbulent shearing stress in the lower layers of the atmosphere

AbstractIt may readily be shown, from elementary arguments, that for steady fluid flow in circular tubes or between parallel plates, the shear stress in the direction of the mean motion varies linearly with the distance from the wall. This result is quite independent of the nature and origin of the fluid resistance and in particular is valid if the flow be turbulent. However, it has been proved by Ertel (1933) that in the lower layers of the atmosphere (1 ⩽ z ⩽ 30 m) the horizontal turbulent shearing stress defined by τ = η (z)∂v/∂z where η(z) is the vertical austausch coefficient and ∂v/∂z the vertical gradient of mean velocity, is to a high degree of approximation independent of the height. In view of the importance of this conclusion in atmospheric turbulence theory, and its obvious difference from the first, it has been thought worth while to examine Ertel's treatment in detail. The latter is based on the assumption of the isotropy of the coefficient of vertical turbulent momentum interchange and the final result depends on the relative smallness of the variation of wind direction with height in the surface layers. Complete neglect of this variation, however, requires a wind velocity constant with height, in which case Ertel's result would become trivial. The object of the present note is to show that the assumption of very small but plausible values for the wind direction change with height in the surface layers (of order 10‐6 radians/cm.) suffices to account for the observed wind velocity increase in the lower layers.It may be concluded that Ertel's analysis is sound. Furthermore it appears on the basis of the theory that the mean wind direction change with height in the lower layers is too small to be observed practically.